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The two data sets in the table below are dependent random samples. The population of (x−y)(x-y)...

The two data sets in the table below are dependent random samples. The population of (x−y)(x-y) differences is approximately normally distributed. A claim is made that the mean difference (x−y)(x-y) is greater than 17.9.

x 67 79 68 52 56 78 78 78
y 30 50 32 49 31 51 37 35

For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.

(a) Calculate the value of the test statistic used in this test.

     Test statistic's value =

(b) Use your calculator to find the P-value of this test.

     P-value =

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.04 significance level. If there are two critical values, then list them both with a comma between them.

     Critical value(s) =

(d) What is the correct conclusion of this hypothesis test at the 0.04 significance level?     

  • There is sufficient evidence to warrant rejection the claim that the mean difference is greater than 17.9
  • There is not sufficient evidence to support the claim that the mean difference is greater than 17.9
  • There is not sufficient evidence to warrant rejection the claim that the mean difference is greater than 17.9
  • There is sufficient evidence to support the claim that the mean difference is greater than 17.9

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